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Balanced realizations of regime-switching linear systems

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Abstract

In this work, we establish a framework for balanced realization of linear systems subject to regime switching modulated by a continuous-time Markov chain with a finite state space. First, a definition of balanced realization is given. Then a ρ-balanced realization is developed to approximate the system of balancing equations, which is a system of time-varying algebraic equations. When the state space of the Markov chain is large, the computational effort becomes a real concern. To resolve this problem, we introduce a two-time-scale formulation and use decomposition/aggregation and averaging techniques to reduce the computational complexity. Based on the two-time-scale formulation, further approximation procedures are developed. Numerical examples are also presented for demonstration.

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Authors and Affiliations

  1. Department of Mathematics, Missouri Southern State University, Joplin, MO, 64801, USA

    Y. J. Liu

  2. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA

    G. Yin

  3. Department of Mathematics, The University of Georgia, Athens, GA, 30602, USA

    Q. Zhang

  4. Department of Systems Engineering, Research School of Information Sciences and Engineering, Australian National University, Canberra, ACT, 0200, Australia

    J. B. Moore

Authors
  1. Y. J. Liu
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  2. G. Yin
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  3. Q. Zhang
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  4. J. B. Moore
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Correspondence to G. Yin.

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Liu, Y.J., Yin, G., Zhang, Q. et al. Balanced realizations of regime-switching linear systems. Math. Control Signals Syst. 19, 207–234 (2007). https://doi.org/10.1007/s00498-007-0019-3

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  • DOI: https://doi.org/10.1007/s00498-007-0019-3

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